power system stability and control chuong (33)

31
Voltage Sags
Math H.J. Bollen
STRI
31.1 Voltage Sag Characteristics 31-1
Voltage Sag Magnitude—Monitoring
.
Origin of Voltage
Sags
.
Voltage Sag Magnitude—Calculation
.
Propagation of
Voltage Sags
.
Critical Distance
.
Voltage Sag Duration
.
Phase-Angle Jumps
.
Three-Phase Unbalance
31.2 Equipment Voltage Tolerance 31-8
Voltage Tolerance Requirement
.
Voltage Tolerance
Performance
.
Single-Phase Rectifiers
.
Three-Phase

Rectifiers
31.3 Mitigation of Voltage Sags 31-13
From Fault to Trip
.
Reducing the Number of Faults
.
Reducing the Fault-Clearing Time
.
Changing the Power
System
.
Installing Mitigation Equipment
.
Improving
Equipment Voltage Tolerance
.
Different Events and
Mitigation Methods
Voltage sags are short duration reductions in rms voltage, mainly caused by short circuits and starting of
large motors. The interest in voltage sags is due to the problems they cause on several types of equipment.
Adjustable-speed drives, process-control equipment, and computers are especially notorious for their
sensitivity (Conrad et al., 1991; McGranaghan et al., 1993). Some pieces of equipment trip when the rms
voltage drops below 90% for longer than one or two cycles. Such a piece of equipment will trip tens of
times a year. If this is the process-control equipment of a paper mill, one can imagine that the costs due
to voltage sags can be enormous. A voltage sag is not as damaging to industry as a (long or short)
interruption, but as there are far more voltage sags than interruptions, the total damage due to sags is
still larger. Another important aspect of voltage sags is that they are hard to mitigate. Short interruptions
and many long interruptions can be prevented via simple, although expensive measures in the local
distribution network. Voltage sags at equipment terminals can be due to short-circuit faults hundreds of
kilometers away in the transmission system. It will be clear that there is no simple method to

prevent them.
31.1 Voltage Sag Characteristics
An example of a voltage sag is shown in Fig. 31.1.
1
The voltage amplitude drops to a value of about 20%
of its pre-event value for about two and a half cycles, after which the voltage recovers again. The event
shown in Fig. 31.1 can be characterized as a voltage sag down to 20% (of the pre-event voltage)
for 2.5 cycles (of the fundamental frequency). This event can be characterized as a voltage sag with a
magnitude of 20% and a duration of 2.5 cycles.
1
The datafile containing these measurements was obtained from a Website with test data set up for IEEE project
group P1159.2: http:== grouper.ieee.org=groups=1159=2=index.html.
ß 2006 by Taylor & Francis Group, LLC.
31.1.1 Voltage Sag Magnitude—Monitoring
The magnitude of a voltage sag is determined from the rms voltage. The rms voltage for the sag in
Fig. 31.1 is shown in Fig. 31.2. The rms voltage has been calculated over a one-cycle sliding window:
V
rms
kðÞ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
N
X
i¼k
i¼kÀN þ1
viðÞ
2
v
u
u

t
(31:1)
with N the number of samples per cycle, and v(i) the sampled voltage in time domain. The rms voltage
as shown in Fig. 31.2 does not immediately drop to a lower value, but takes one cycle for the transition.
1
0.8
0.6
0.4
0.2
0
0123
Time in cycles
Voltage in pu
456
−0.2
−0.4
−0.6
−0.8
−1
FIGURE 31.1 A voltage sag—voltage in one phase in time domain.
1
0.8
0.6
0.4
0.2
0
0123
Time in cycles
Voltage in pu
456

FIGURE 31.2 One-cycle rms voltage for the voltage sag shown in Fig. 31.1.
ß 2006 by Taylor & Francis Group, LLC.
This is due to the finite length of the window used to calculate the rms value. We also see that the rms
value during the sag is not completely constant and that the voltage does not immediately recover
after the fault.
There are various ways of obtaining the sag magnitude from the rms voltages. Most power quality
monitors take the lowest value obtained during the event. As sags normally have a constant rms value
during the deep part of the sag, using the lowest value is an acceptable approximation.
The sag is characterized through the remaining voltage during the event. This is then given as a
percentage of the nominal voltage. Thus, a 70% sag in a 230-V system means that the voltage
dropped to 161 V. The confusion with this terminology is clear. One could be tricked into thinking
that a 70% sag refers to a drop of 70%, thus a remaining voltage of 30%. The recommendation is
therefore to use the phrase ‘‘a sag down to 70%.’’ Characterizing the sag through the actual drop in
rms voltage can solve this ambiguity, but this will introduce new ambiguities like the choice of the
reference voltage.
31.1.2 Origin of Voltage Sags
Consider the distribution network shown in Fig. 31.3, where the numbers (1 through 5) indicate fault
positions and the letters (A through D) loads. A fault in the transmission network, fault position 1, will
cause a serious sag for both substations bordering the faulted line. This sag is transferred down to all
customers fed from these two substations. As there is normally no generation connected at lower voltage
levels, there is nothing to keep up the voltage. The result is that all customers (A, B, C, and D) experience
a deep sag. The sag experienced by A is likely to be somewhat less deep, as the generators connected to
that substation will keep up the voltage. A fault at position 2 will not cause much voltage drop for
customer A. The impedance of the transformers between the transmission and the subtransmission
system are large enough to considerably limit the voltage drop at high-voltage side of the transformer.
The sag experienced by customer A is further mitigated by the generators feeding into its local
transmission substation. The fault at position 2 will, however, cause a deep sag at both subtransmission
substations and thus for all customers fed from here (B, C, and D). A fault at position 3 will cause a short
or long interruption for customer D when the protection clears the fault. Customer C will only
experience a deep sag. Customer B will experience a shallow sag due to the fault at position 3, again

due to the transformer impedance. Customer A will probably not notice anything from this fault. Fault 4
causes a deep sag for customer C and a shallow one for customer D. For fault 5, the result is the other
way around: a deep sag for customer D and a shallow one for customer C. Customers A and B will not
experience any significant drop in voltage due to
faults 4 and 5.
31.1.3 Voltage Sag Magnitude—
Calculation
To quantify sag magnitude in radial systems, the
voltage divider model, shown in Fig. 31.4, can be
used, where Z
S
is the source impedance at the point-
of-common coupling; and Z
F
is the impedance
between the point-of-common coupling and the
fault. The point-of-common coupling (pcc) is
the point from which both the fault and the load
are fed. In other words, it is the place where the load
current branches off from the fault current. In the
voltage divider model, the load current before, as
well as during the fault is neglected. The voltage at
the pcc is found from:
transmission
subtransmisson
distribution
low voltage
1
2
A

B
3
D
5
4
C
FIGURE 31.3 Distribution network with load posi-
tions (A through D) and fault positions (1 through 5).
ß 2006 by Taylor & Francis Group, LLC.
V
sag
¼
Z
F
Z
S
þ Z
F
(31:2)
where it is assumed that the pre-event voltage is
exactly 1 pu, thus E ¼1. The same expression can
be derived for constant-impedance load, where E is
the pre-event voltage at the pcc. We see from
Eq. (31.2) that the sag becomes deeper for faults
electrically closer to the customer (when Z
F
be-
comes smaller), and for weaker systems (when Z
S
becomes larger).

Equation (31.2) can be used to calculate the sag magnitude as a function of the distance to the fault.
Therefore, we write Z
F
¼zd, with z the impedance of the feeder per unit length and d the distance
between the fault and the pcc, leading to:
V
sag
¼
zd
Z
S
þ zd
(31:3)
This expression has been used to calculate the sag magnitude as a function of the distance to the
fault for a typical 11 kV overhead line, resulting in Fig. 31.5. For the calculations, a 150-mm
2
overhead line was used and fault levels of 750 MVA, 200 MVA, and 75 MVA. The fault level is used
to calculate the source impedance at the pcc and the feeder impedance is used to calculate the
impedance between the pcc and the fault. It is assumed that the source impedance is purely
reactive, thus Z
S
¼j 0.161 V for the 750 MVA source. The impedance of the 150 mm
2
overhead
line is z ¼0.117 þj 0.315 V=km.
31.1.4 Propagation of Voltage Sags
It is also possible to calculate the sag magnitude directly from fault levels at the pcc and at the fault
position. Let S
FLT
be the fault level at the fault position and S

PCC
at the point-of-common coupling. The
voltage at the pcc can be written as:
E
Z
S
V
Sag
Z
F
pcc
load
fault
FIGURE 31.4 Voltage divider model for a voltage sag.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 102030
750 MVA
200 MVA
75 MVA
Distance to the fault in km

Sag magnitude in pu
40 50
FIGURE 31.5 Sag magnitude as a function of the distance to the fault.
ß 2006 by Taylor & Francis Group, LLC.
V
sag
¼ 1 À
S
FLT
S
PCC
(31:4)
This equation can be used to calculate the magnitude of sags due to faults at voltage levels other than
the point-of-common coupling. Consider typical fault levels as shown in Table 30.1. This data has been
used to obtain Table 30.2, showing the effect of a short circuit fault at a lower voltage level than the pcc.
We can see that sags are significantly ‘‘damped’’ when they propagate upwards in the power system. In a
sags study, we typically only have to take faults one voltage level down from the pcc into account. And
even those are seldom of serious concern. Note, however, that faults at a lower voltage level may be
associated with a longer fault-clearing time and thus a longer sag duration. This especially holds for
faults on distribution feeders, where fault-clearing times in excess of one second are possible.
31.1.5 Critical Distance
Equation (31.3) gives the voltage as a function of distance to the fault. From this equation we can obtain
the distance at which a fault will lead to a sag of a certain magnitude V. If we assume equal X=R ratio of
source and feeder, we get the following equation:
d
crit
¼
Z
S
z

Â
V
1 À V
(31:5)
We refer to this distance as the critical distance. Suppose that a piece of equipment trips when the
voltage drops below a certain level (the critical voltage). The definition of critical distance is such that
each fault within the critical distance will cause the equipment to trip. This concept can be used to
estimate the expected number of equipment trips due to voltage sags (Bollen, 1998). The critical distance
has been calculated for different voltage levels, using typical fault levels and feeder impedances. The data
used and the results obtained are summarized in Table 30.3 for the critical voltage of 50%. Note how the
critical distance increases for higher voltage levels. A customer will be exposed to much more kilometers
of transmission lines than of distribution feeder. This effect is understood by writing Eq. (31.5) as a
function of the short-circuit current I
flt
at the pcc:
d
crit
¼
V
nom
zI
flt
Â
V
1 À V
(31:6)
TABLE 30.1 Typical Fault Levels at Different Voltage Levels
Voltage Level Fault Level
400 V 20 MVA
11 kV 200 MVA

33 kV 900 MVA
132 kV 3000 MVA
400 kV 17,000 MVA
TABLE 30.2 Propagation of Voltage Sags to Higher Voltage Levels
Point-of-Common Coupling at:
Fault at: 400 V 11 kV 33 kV 132 kV 400 kV
400 V — 90% 98% 99% 100%
11 kV — — 78% 93% 99%
33 kV — — — 70% 95%
132 kV — — — — 82%
ß 2006 by Taylor & Francis Group, LLC.
with V
nom
the nominal voltage. As both z and I
flt
are of similar magnitude for different voltage levels, one
can conclude from Eq. (31.6) that the critical distance increases proportionally with the voltage level.
31.1.6 Voltage Sag Duration
It was shown before, the drop in voltage during a sag is due to a short circuit being present in the system.
The moment the short circuit fault is cleared by the protection, the voltage starts to return to its original
value. The duration of a sag is thus determined by the fault-clearing time. However, the actual duration
of a sag is normally longer than the fault-clearing time.
Measurement of sag duration is less trivial than it might appear. From a recording the sag duration
may be obvious, but to come up with an automatic way for a power quality monitor to obtain the sag
duration is no longer straightforward. The commonly used definition of sag duration is the number of
cycles during which the rms voltage is below a given threshold. This threshold will be somewhat different
for each monitor but typical values are around 90% of the nominal voltage. A power quality monitor
will typically calculate the rms value once every cycle.
The main problem is that the so-called post-fault sag will affect the sag duration. When the fault is
cleared, the voltage does not recover immediately. This is mainly due to the reenergizing and reaccelera-

tion of induction motor load (Bollen, 1995). This post-fault sag can last several seconds, much longer
than the actual sag. Therefore, the sag duration as defined before, is no longer equal to the fault-
clearing time. More seriously, different power quality monitors will give different values for the sag
duration. As the rms voltage recovers slowly, a small difference in threshold setting may already lead to a
serious difference in recorded sag duration (Bollen, 1999).
Generally speaking, faults in transmission systems are cleared faster than faults in distribution
systems. In transmission systems, the critical fault-clearing time is rather small. Thus, fast protection
and fast circuit breakers are essential. Also, transmission and subtransmission systems are normally
operated as a grid, requiring distance protection or differential protection, both of which allow for fast
clearing of the fault. The principal form of protection in distribution systems is overcurrent protection.
This requires a certain amount of time-grading, which increases the fault-clearing time. An exception is
formed by systems in which current-limiting fuses are used. These have the ability to clear a fault within
one half-cycle. In overhead distribution systems, the instantaneous trip of the recloser will lead to a short
sag duration, but the clearing of a permanent fault will give a sag of much longer duration.
The so-called magnitude-duration plot is a common tool used to show the quality of supply at a
certain location or the average quality of supply of a number of locations. Voltage sags due to faults can
be shown in such a plot, as well as sags due to motor starting, and even long and short interruptions.
Different underlying causes lead to events in different parts of the magnitude-duration plot, as shown in
Fig. 31.6.
31.1.7 Phase-Angle Jumps
A short circuit in a power system not only causes a drop in voltage magnitude, but also a change in
the phase angle of the voltage. This sudden change in phase angle is called a ‘‘phase-angle jump.’’ The
phase-angle jump is visible in a time-domain plot of the sag as a shift in voltage zero-crossing between
TABLE 30.3 Critical Distance for Faults at Different Voltage Levels
Nominal Voltage Short-Circuit Level Feeder Impedance Critical Distance
400 V 20 MVA 230 mV=km 35 m
11 kV 200 MVA 310 mV=km 2 km
33 kV 900 MVA 340 mV=km 4 km
132 kV 3000 MVA 450 mV=km 13 km
400 kV 10000 MVA 290 mV=km 55 km

ß 2006 by Taylor & Francis Group, LLC.
the pre-event and the during-event voltage. With reference to Fig. 31.4 and Eq. (31.2), the phase-angle
jump is the argument of V
sag
, thus the difference in argument between Z
F
and Z
S
þZ
F
. If source and
feeder impedance have equal X=R ratio, there will be no phase-angle jump in the voltage at the pcc. This
is the case for faults in transmission systems, but normally not for faults in distribution systems. The
latter may have phase-angle jumps up to a few tens of degrees (Bollen, 1999; Bollen et al., 1996).
Figure 31.4 shows a single-phase circuit, which is a valid model for three-phase faults in a three-phase
system. For nonsymmetrical faults, the analysis becomes much more complicated. A consequence of
nonsymmetrical faults (single-phase, phase-to-phase, two-phase-to-ground) is that single-phase load
experiences a phase-angle jump even for equal X=R ratio of feeder and source impedance (Bollen, 1999;
Bollen, 1997).
To obtain the phase-angle jump from the measured voltage waveshape, the phase angle of the voltage
during the event must be compared with the phase angle of the voltage before the event. The phase angle
of the voltage can be obtained from the voltage zero-crossings or from the argument of the fundamental
component of the voltage. The fundamental component can be obtained by using a discrete Fourier
transform algorithm. Let V
1
(t) be the fundamental component obtained from a window (t-T,t), with
T one cycle of the power frequency, and let t ¼0 correspond to the moment of sag initiation. In case
there is no chance in voltage magnitude or phase angle, the fundamental component as a function of
time is found from:
V

1
tðÞ¼V
1
0ðÞe
jvt
(31:7)
The phase-angle jump, as a function of time, is the difference in phase angle between the actual
fundamental component and the ‘‘synchronous voltage’’ according to Eq. (31.7):
f tðÞ¼arg V
1
tðÞ
fg
À arg V
1
0ðÞe
jvt
ÈÉ
¼ arg
V
1
t
ðÞ
V
1
0
ðÞ
e
Àjvt
&'
(31:8)

Note that the argument of the latter expression is always between –1808 and þ1808.
31.1.8 Three-Phase Unbalance
For three-phase equipment, three voltages need to be considered when analyzing a voltage sag event
at the equipment terminals. For this, a characterization of three-phase unbalanced voltage sags is
100%
80%
50%
0%
0.1 s
1 sec
Duration
Magnitude
interruptions
motor starting
remote
MV networks
local
MV network
transmission
network
fuses
FIGURE 31.6 Sags of different origin in a magnitude-duration plot.
ß 2006 by Taylor & Francis Group, LLC.
introduced. The basis of this characterization is the theory of symmetrical components. Instead of the
three-phase voltages or the three symmetrical components, the following three (complex) values are
used to characterize the voltage sag (Bollen and Zhang, 1999; Zhang and Bollen, 1998):
.
The ‘‘characteristic voltage’’ is the main characteristic of the event. It indicates the severity of the
sag, and can be treated in the same way as the remaining voltage for a sag experienced by a single-
phase event.

.
The ‘‘PN factor’’ is a correction factor for the effect of the load on the voltages during the event.
The PN factor is normally close to unity and can then be neglected. Exceptions are systems with a
large amount of dynamic load, and sags due to two-phase-to-ground faults.
.
The ‘‘zero-sequence voltage,’’ which is normally not transferred to the equipment terminals, rarely
affects equipment behavior. The zero-sequence voltage can be neglected in most studies.
Neglecting the zero-sequence voltage, it can be shown that there are two types of three-phase
unbalanced sags, denoted as types C and D. Type A is a balanced sag due to a three-phase fault. Type
B is the sag due to a single-phase fault, which turns into type D after removal of the zero-sequence
voltage. The three complex voltages for a type C sag are written as follows:
V
a
¼ F
V
b
¼À
1
2
F À
1
2
jV
ffiffiffi
3
p
V
c
¼À
1

2
F þ
1
2
jV
ffiffiffi
3
p
(31:9)
where V is the characteristic voltage and F the PN factor. The (characteristic) sag magnitude is defined as
the absolute value of the characteristic voltage; the (characteristic) phase-angle jump is the argument of
the characteristic voltage. For a sag of type D, the expressions for the three voltage phasors are as follows:
V
a
¼ V
V
b
¼À
1
2
V À
1
2
jF
ffiffiffi
3
p
V
c
¼À

1
2
V þ
1
2
jF
ffiffiffi
3
p
(31:10)
Sag type D is due to a phase-to-phase fault, or due to a single-phase fault behind a Dy-transformer, or
a phase-to-phase fault behind two Dy-transformers, etc. Sag type C is due to a single-phase fault, or due
to a phase-to-phase fault behind a Dy-transformer, etc. When using characteristic voltage for a three-
phase unbalanced sag, the same single-phase scheme as in Fig. 31.4 can be used to study the transfer of
voltage sags in the system (Bollen, 1999; Bollen, 1997).
31.2 Equipment Voltage Tolerance
31.2.1 Voltage Tolerance Requirement
Generally speaking, electrical equipment prefers a constant rms voltage. That is what the equipment has
been designed for and that is where it will operate best. The other extreme is zero voltage for a longer
period of time. In that case the equipment will simply stop operating completely. For each piece of
equipment there is a maximum interruption duration, after which it will continue to operate correctly.
A rather simple test will give this duration. The same test can be done for a voltage of 10% (of nominal),
for a voltage of 20%, etc. If the voltage becomes high enough, the equipment will be able to operate on it
indefinitely. Connecting the points obtained by performing these tests results in the so-called ‘‘voltage-
tolerance curve’’ (Key, 1979). An example of a voltage-tolerance curve is shown in Fig. 31.7: the
ß 2006 by Taylor & Francis Group, LLC.
requirements for IT-equipment as recommended by the Information Technology Industry Council
(ITIC, 1999). Strictly speaking, one can claim that this is not a voltage-tolerance curve as described
above, but a requirement for the voltage tolerance. One could refer to this as a voltage-tolerance
requirement and to the result of equipment tests as a voltage-tolerance performance. We see in

Fig. 31.7 that IT equipment has to withstand a voltage sag down to zero for 1.1 cycle, down to 70%
for 30 cycles, and that the equipment should be able to operate normally for any voltage of 90%
or higher.
31.2.2 Voltage Tolerance Performance
Voltage-tolerance (performance) curves for personal computers are shown in Fig. 31.8. The curves are
the result of equipment tests performed in the U.S. (EPRI, 1994) and in Japan (Sekine et al., 1992). The
shape of all the curves in Fig. 13.8 is close to rectangular. This is typical for many types of equipment, so
that the voltage tolerance may be given by only two values, maximum duration and minimum voltage,
100
80
60
40
20
0
0.1 1 10
Duration in (60Hz) Cycles
Magnitude in %
100 1000
FIGURE 31.7 Voltage-tolerance requirement for IT equipment.
100
80
60
40
20
0
0 100 200
Duration in ms
Magnitude in percent
300 400
FIGURE 31.8 Voltage-tolerance performance for personal computers.

ß 2006 by Taylor & Francis Group, LLC.
instead of by a full curve. From the tests summarized in Fig. 13.8 it is found that the voltage tolerance of
personal computers varies over a wide range: 30–170 ms, 50–70% being the range containing half of the
models. The extreme values found are 8 ms, 88% and 210 ms, 30%.
Voltage-tolerance tests have also been performed on process-control equipment: PLCs, monitoring
relays, motor contactors. This equipment is even more sensitive to voltage sags than personal computers.
The majority of devices tested tripped between one and three cycles. A small minority was able to
tolerate sags up to 15 cycles in duration. The minimum voltage varies over a wider range: from 50% to
80% for most devices, with exceptions of 20% and 30%. Unfortunately, the latter two both tripped in
three cycles (Bollen, 1999).
From performance testing of adjustable-speed drives, an ‘‘average voltage-tolerance curve’’ has been
obtained. This curve is shown in Fig. 31.9. The sags for which the drive was tested are indicated as
circles. It has further been assumed that the drives can operate indefinitely on 85% voltage. Voltage
tolerance is defined here as ‘‘automatic speed recovery, without reaching zero speed.’’ For sensitive
production processes, more strict requirements will hold (Bollen, 1999).
31.2.3 Single-Phase Rectifiers
The sensitivity of most single-phase equipment can be understood from the equivalent scheme in
Fig. 31.10. The power supply to a computer, process-control equipment, consumer electronics, etc.
consists of a single-phase (four-pulse) rectifier together with a capacitor and a DC=DC converter.
During normal operation the capacitor is charged twice a cycle through the diodes. The result is a DC
voltage ripple:
e ¼
PT
2V
2
0
C
(31:11)
with P the DC bus active-power load, T one cycle of the power frequency, V
0

the maximum DC bus
voltage, and C the size of the capacitor.
During a voltage sag or interruption, the capacitor continues to discharge until the DC bus voltage has
dropped below the peak of the supply voltage. A new steady state is reached, but at a lower DC bus
100%
85%
70%
50%
33ms
100ms
170ms 1000ms
Magnitude
Duration
FIGURE 31.9 Average voltage-tolerance curve for adjustable-speed drives.
ß 2006 by Taylor & Francis Group, LLC.
voltage and with a larger ripple. The resulting DC bus voltage for a sag down to 50% is shown in
Fig. 31.11, together with the absolute value of the supply voltage. If the new steady state is below the
minimum operating voltage of the DC=DC converter, or below a certain protection setting, the
equipment will trip. During the decaying DC bus voltage, the capacitor voltage V(t) can be obtained
from the law of conservation of energy:
1
2
CV
2
¼
1
2
CV
2
0

À Pt (31:12)
where a constant DC bus load P has been assumed. From Eq. (31.12) the voltage as a function of time is
obtained:
VtðÞ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
V
2
0
À
2P
C
t
r
(31:13)
Combining this with Eq. (31.11) gives the following expression:
VtðÞ¼V
0
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 À 4e
t
T
r
(31:14)
230 V ac
non-regulated dc voltage
regulated
dc voltage
voltage
controller
FIGURE 31.10 Typical power supply to sensitive single-phase equipment.

1
0.8
0.6
0.4
0.2
0
024
Time in cycles
Voltage
6810
FIGURE 31.11 Absolute value of AC voltage (dashed) and DC bus voltage (solid line) for a sag down to 50%.
ß 2006 by Taylor & Francis Group, LLC.
The larger the DC ripple in normal operation, the faster the drop in DC bus voltage during a sag. From
Eq. (31.14) the maximum duration of zero voltage t
max
is calculated for a minimum operating voltage
V
min
, resulting in:
t
max
¼
1 À
V
min
V
0

2
4e

T (31:15)
31.2.4 Three-Phase Rectifiers
The performance of equipment fed through three-phase rectifiers becomes somewhat more compli-
cated. The main equipment belonging to this category is formed by AC and DC adjustable-speed
drives. One of the complications is that the operation of the equipment is affected by the three voltages,
which are not necessarily the same during the voltage sag. For non-controlled (six pulse) diode rectifiers,
a similar model can be used as for single-phase rectifiers. The operation of three-phase controlled
rectifiers can become very complicated and application-specific (Bollen, 1996). Therefore, only non-
controlled rectifiers will be discussed here. For voltage sags due to three-phase faults, the DC bus voltage
behind the (three-phase) rectifier will decay until a new steady state is reached at a lower voltage level,
with a larger ripple. To calculate the DC bus voltage as a function of time, and the time-to-trip, the same
equation as for the single-phase rectifier can be used.
For unbalanced voltage sags, a distinction needs to be made between the two types (C and D), as
introduced in the section on Three-Phase Unbalance. Figure 31.12 shows AC and DC side voltages for a
sag of type C with V ¼0.5 pu and F ¼1. For this sag, the voltage drops in two phases where the third
phase stays at its presag value. Three capacitor sizes are used (Bollen and Zhang, 1999); a ‘‘large’’
capacitance is defined as a value that leads to an initial decay of the DC voltage equal to 10%, which is
433 F=kW for a 620 V drive. In the same way, ‘‘small’’ capacitance corresponds to 75% per cycle initial
decay, and 57.8 F=kW for a 620 V drive. It turns out that even for the small capacitance, the DC bus
voltage remains above 70%. For the large capacitance value, the DC bus voltage is hardly affected by the
voltage sag. It is easy to understand that this is also the case for type C sags with an even lower
characteristic magnitude V (Bollen, 1999; Bollen and Zhang, 1999).
0
0.4
0.6
0.8
1
−1
0
1

−0.5
0.5
0.5 1 1.5
Time in cycles
DC bus voltage AC bus voltage
2.523
0 0.5 1 1.5 2.523
FIGURE 31.12 AC and DC side voltages for a three-phase rectifier during a sag of type C.
ß 2006 by Taylor & Francis Group, LLC.
Figure 31.13 shows the equivalent results for a sag of type D, again with V ¼0.5 and F ¼1. As all three
AC voltages show a drop in voltage magnitude, the DC bus voltage will drop even for a large capacitor.
But the effect is still much less than for a three-phase (balanced) sag.
The effect of a lower PN factor (F < 1) is that even the highest voltage shows a drop for a type C sag,
so that the DC bus voltage will always show a small drop. Also for a type D sag, a lower PN factor will
lead to an additional drop in DC bus voltage (Bollen and Zhang, 1999).
31.3 Mitigation of Voltage Sags
31.3.1 From Fault to Trip
To understand the various ways of mitigation, the mechanism leading to an equipment trip needs to
be understood. The equipment trip is what makes the event a problem; if there are no equipment
trips, there is no voltage sag problem. The underlying event of the equipment trip is a short-circuit
fault. At the fault position, the voltage drops to zero, or to a very low value. This zero voltage is
changed into an event of a certain magnitude and duration at the interface between the equipment
and the power system. The short-circuit fault will always cause a voltage sag for some customers. If
the fault takes place in a radial part of the system, the protection intervention clearing the
fault will also lead to an interruption. If there is sufficient redundancy present, the short circuit
will only lead to a voltage sag. If the resulting event exceeds a certain severity, it will cause an
equipment trip.
Based on this reasoning, it is possible to distinguish between the following mitigation methods:
.
Reducing the number of short-circuit faults.

.
Reducing the fault-clearing time.
.
Changing the system such that short-circuit faults result in less severe events at the equipment
terminals or at the customer interface.
.
Connecting mitigation equipment between the sensitive equipment and the supply.
.
Improving the immunity of the equipment.
0.4
0 0.5 1 21.5
Time in c
y
cles
2.5 3
0 0.5 1 21.5 2.5 3
0.6
DC bus voltage
AC bus voltage
0.8
1
1
0.5
−0.5
−1
0
FIGURE 31.13 AC and DC side voltages for a three-phase rectifier during a sag of type D.
ß 2006 by Taylor & Francis Group, LLC.
31.3.2 Reducing the Number of Faults
Reducing the number of short-circuit faults in a system not only reduces the sag frequency, but also the

frequency of long interruptions. This is thus a very effective way of improving the quality of supply and
many customers suggest this as the obvious solution when a voltage sag or interruption problem occurs.
Unfortunately, most of the time the solution is not that obvious. A short circuit not only leads to a
voltage sag or interruption at the customer interface, but may also cause damage to utility equipment
and plant. Therefore, most utilities will already have reduced the fault frequency as far as economically
feasible. In individual cases, there could still be room for improvement, e.g., when the majority of trips
are due to faults on one or two distribution lines. Some examples of fault mitigation are:
.
Replace overhead lines by underground cables.
.
Use special wires for overhead lines.
.
Implement a strict policy of tree trimming.
.
Install additional shielding wires.
.
Increase maintenance and inspection frequencies.
One has to keep in mind, however, that these measures can be very expensive, especially for
transmission systems, and that their costs have to be weighted against the consequences of the
equipment trips.
31.3.3 Reducing the Fault-Clearing Time
Reducing the fault-clearing time does not reduce the number of events, but only their severity. It does
not do anything to reduce to number of interruptions, but can significantly limit the sag duration.
The ultimate reduction of fault-clearing time is achieved by using current-limiting fuses, able to clear
a fault within one half-cycle. The recently introduced static circuit breaker has the same characteristics:
fault-clearing time within one half-cycle. Additionally, several types of fault-current limiters have
been proposed that do not actually clear the fault, but significantly reduce the fault current magnitude
within one or two cycles. One important restriction of all these devices is that they can only be used for
low- and medium-voltage systems. The maximum operating voltage is a few tens of kilovolts.
But the fault-clearing time is not only the time needed to open the breaker, but also the time needed

for the protection to make a decision. To achieve a serious reduction in fault-clearing time, it is necessary
to reduce any grading margins, thereby possibly allowing for a certain loss of selectivity.
31.3.4 Changing the Power System
By implementing changes in the supply system, the severity of the event can be reduced. Here again, the
costs may become very high, especially for transmission and subtransmission voltage levels. In industrial
systems, such improvements more often outweigh the costs, especially when already included in the
design stage. Some examples of mitigation methods especially directed toward voltage sags are:
.
Install a generator near the sensitive load. The generators will keep up the voltage during a remote
sag. The reduction in voltage drop is equal to the percentage contribution of the generator station
to the fault current. In case a combined-heat-and-power station is planned, it is worth it to
consider the position of its electrical connection to the supply.
.
Split buses or substations in the supply path to limit the number of feeders in the exposed area.
.
Install current-limiting coils at strategic places in the system to increase the ‘‘electrical distance’’ to
the fault. The drawback of this method is that this may make the event worse for other customers.
.
Feed the bus with the sensitive equipment from two or more substations. A voltage sag in one
substation will be mitigated by the infeed from the other substations. The more independent the
substations are, the more the mitigation effect. The best mitigation effect is by feeding from two
different transmission substations. Introducing the second infeed increases the number of sags,
but reduces their severity.
ß 2006 by Taylor & Francis Group, LLC.
31.3.5 Installing Mitigation Equipment
The most commonly applied method of mitigation is the installation of additional equipment at the
system-equipment interface. Also recent developments point toward a continued interest in this way of
mitigation. The popularity of mitigation equipment is explained by it being the only place where the
customer has control over the situation. Both changes in the supply as well as improvement of the
equipment are often completely outside of the control of the end user. Some examples of mitigation

equipment are:
.
Uninterruptable power supply (UPS). This is the most commonly used device to protect low-
power equipment (computers, etc.) against voltage sags and interruptions. During the sag or
interruption, the power supply is taken over by an internal battery. The battery can supply the
load for, typically, between 15 and 30 minutes.
.
Static transfer switch. A static transfer switch switches the load from the supply with the sag to
another supply within a few milliseconds. This limits the duration of a sag to less than one half-
cycle, assuming that a suitable alternate supply is available.
.
Dynamic voltage restorer (DVR). This device uses modern power electronic components to insert
a series voltage source between the supply and the load. The voltage source compensates for the
voltage drop due to the sag. Some devices use internal energy storage to make up for the drop in
active power supplied by the system. They can only mitigate sags up to a maximum duration.
Other devices take the same amount of active power from the supply by increasing the current.
These can only mitigate sags down to a minimum magnitude. The same holds for devices
boosting the voltage through a transformer with static tap changer.
.
Motor-generator sets. Motor-generator sets are the classical solution for sag and interruption
mitigation with large equipment. They are obviously not suitable for an office environment but
the noise and the maintenance requirements are often no problem in an industrial environment.
Some manufacturers combine the motor-generator set with a backup generator; others combine
it with power-electronic converters to obtain a longer ride-through time.
31.3.6 Improving Equipment Voltage Tolerance
Improvement of equipment voltage tolerance is probably the most effective solution against equipment
trips due to voltage sags. But as a short-time solution, it is often not suitable. In many cases, a customer
only finds out about equipment performance after it has been installed. Even most adjustable-speed
drives have become off-the-shelf equipment where the customer has no influence on the specifications.
Only large industrial equipment is custom-made for a certain application, which enables the incorpor-

ation of voltage-tolerance requirements in the specification.
Apart from improving large equipment (drives, process-control computers), a thorough inspection of
the immunity of all contactors, relays, sensors, etc. can significantly improve the voltage tolerance of the
process.
31.3.7 Different Events and Mitigation Methods
Figure 31.6 showed the magnitude and duration of voltage sags and interruptions resulting from various
system events. For different events, different mitigation strategies apply.
Sags due to short-circuit faults in the transmission and subtransmission system are characterized by a
short duration, typically up to 100 ms. These sags are very hard to mitigate at the source and
improvements in the system are seldom feasible. The only way of mitigating these events is by
improvement of the equipment or, where this turns out to be unfeasible, installing mitigation equip-
ment. For low-power equipment, a UPS is a straightforward solution; for high-power equipment and for
complete installations, several competing tools are emerging.
The duration of sags due to distribution system faults depends on the type of protection
used—ranging from less than a cycle for current-limiting fuses up to several seconds for overcurrent
ß 2006 by Taylor & Francis Group, LLC.
relays in underground or industrial distribution systems. The long sag duration also enables equip-
ment to trip due to faults on distribution feeders fed from other HV=MV substations. For deep
long-duration sags, equipment improvement becomes more difficult and system improvement easier.
The latter could well become the preferred solution, although a critical assessment of the various options
is certainly needed.
Sags due to faults in remote distribution systems and sags due to motor starting should not lead to
equipment tripping for sags down to 85%. If there are problems, the equipment needs to be improved. If
equipment trips occur for long-duration sags in the 70–80% magnitude range, changes in the system
have to be considered as an option.
For interruptions, especially the longer ones, equipment improvement is no longer feasible. System
improvements or a UPS in combination with an emergency generator are possible solutions here.
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